You're just missing some compiler flags to include the proper libraries. As danielko said, a quick google search on the missing libraries brings up some suggestions. E.g.
Linux c++ error: undefined reference to 'dlopen'
http://sourceforge.net/p/dev-cpp/discussion/48211/thread/3bd8b8a1
These suggest your compilation should be something more like:
cc -o demo demo.c -ldl -llpsolve55
and the lpsolve documentation suggests a command that includes the project directory such as:
cc -I/lp_solve_5.5 -I/lp_solve_5.5/bfp -I/lp_solve_5.5/bfp/bfp_etaPFI -I/lp_solve_5.5/colamd $src -o MyExe.exe -lm -ldl